Giant planets dominate the mass of many planetary systems, including the Solar System, and represent the best-characterized class of extrasolar planets. Understanding the formation of giant planets bridges the high mass end of the planet formation process and the low mass end of processes that produce stellar and brown dwarf companions. This review examines the latest evidence supporting the formation of Solar System giant planets and most extrasolar giant planets by core accretion. Key elements of this theory and recent advances are discussed, along with the role of gravitational fragmentation of gas disks – a mechanism more likely to produce brown dwarfs and/or similarly massive binary companions.